A guitar string with a linear mass density of 2.0 g/m is stretched between two vertical rods that are 65 cm apart. The string holds a standing wave, fixed at both ends, with three antinodes when it oscillates at a frequency of 430 HzWhat is the frequency of the fifth harmonic of this string?

Question

Physics

Mini

30 November, 13:16

A guitar string with a linear mass density of 2.0 g/m is stretched between two vertical rods that are 65 cm apart. The string holds a standing wave, fixed at both ends, with three antinodes when it oscillates at a frequency of 430 HzWhat is the frequency of the fifth harmonic of this string?

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Answers (1)

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Parker · Answer 1

717 Hz

Explanation:

solution:

The wave with three antinodes has m = 3. Thus, f_3 = 3f_1 and so the fundamental frequency of the string is

f_1 = f_3/3

=430 Hz/3

=143 Hz

Thus, the frequency of the fifth harmonic is

f_5 = 5*f_1

= 5*143 Hz

= 717 Hz